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arXiv · 1012.1789

Distribution of relative velocities in turbulent aerosols

K. Gustavsson·B. Mehlig
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Abstract

We compute the distribution of relative velocities for a one-dimensional model of heavy particles suspended in a turbulent flow, quantifying the caustic contribution to the moments of relative velocities. The same principles determine the corresponding caustic contribution in $d$ spatial dimensions. The distribution of relative velocities Δv at small separations R acquires the universal form ρ(Δv,R) ~ R^{d-1}|Δv|^{D_2-2d} for large (but not too large) values of |Δv|. Here D_2 is the phase-space correlation dimension. Our conclusions are in excellent agreement with numerical simulations of particles suspended in a randomly mixing flow in two dimensions, and in quantitative agreement with published data on direct numerical simulations of particles in turbulent flows.

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K. Gustavsson, B. Mehlig. 2012-06-09. Distribution of relative velocities in turbulent aerosols. https://doi.org/10.1103/physreve.84.045304

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